\left\{ \begin{array} { l } { x = y + 2z } \\ { 3 x - z = 7 } \\ { 3 z - y = 7 } \end{array} \right.

$⎩⎪⎨⎪⎧ x=y+2z3x−z=73z−y=7 $

Solve for x, y, z

x=3<br/>y=-1<br/>z=2

$x=3$

$y=−1$

$z=2$

$y=−1$

$z=2$

Copy

Copied to clipboard

3\left(y+2z\right)-z=7

Substitute y+2z for x in the equation 3x-z=7.

y=\frac{7}{3}-\frac{5}{3}z z=\frac{7}{3}+\frac{1}{3}y

Solve the second equation for y and the third equation for z.

z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right)

Substitute \frac{7}{3}-\frac{5}{3}z for y in the equation z=\frac{7}{3}+\frac{1}{3}y.

z=2

Solve z=\frac{7}{3}+\frac{1}{3}\left(\frac{7}{3}-\frac{5}{3}z\right) for z.

y=\frac{7}{3}-\frac{5}{3}\times 2

Substitute 2 for z in the equation y=\frac{7}{3}-\frac{5}{3}z.

y=-1

Calculate y from y=\frac{7}{3}-\frac{5}{3}\times 2.

x=-1+2\times 2

Substitute -1 for y and 2 for z in the equation x=y+2z.

x=3

Calculate x from x=-1+2\times 2.

x=3 y=-1 z=2

The system is now solved.

Similar Problems

\left\{ \begin{array} { l } { 8 x + 2 y = 46 } \\ { 7 x + 3 y = 47 } \end{array} \right.

${8x+2y=467x+3y=47 $

\left\{ \begin{array} { l } { 3 x = 24 } \\ { x + 3 y = 17 } \end{array} \right.

${3x=24x+3y=17 $

\left\{ \begin{array} { l } { x = 5y + 5 } \\ { 6 x - 4 y = 7 } \end{array} \right.

${x=5y+56x−4y=7 $

\left\{ \begin{array} { l } { x = y + 2z } \\ { 3 x - z = 7 } \\ { 3 z - y = 7 } \end{array} \right.

$⎩⎪⎨⎪⎧ x=y+2z3x−z=73z−y=7 $

\left\{ \begin{array} { l } { a + b + c + d = 20 } \\ { 3a -2c = 3 } \\ { b + d = 6} \\ { c + b = 8 } \end{array} \right.

$⎩⎪⎪⎪⎨⎪⎪⎪⎧ a+b+c+d=203a−2c=3b+d=6c+b=8 $